Thermodynamics: Object 1 in contact with Object 2

[p1mpz0r]

Homework Statement

After some digging, you locate your aluminum baseball bat (1.3 kg, c = 0.90 kJ/KgK) in a snowbank(0 Celsius) and bring it into a warm (25 Celsius) room. If the 64 m^3 room contains 76 kg of air (c = 1.02 kJ/KgK) and no one goes in or out of the (closed) room, what is the temperature of the bat the next day?

Homework Equations

Q = c m (Tf - Ti)

The Attempt at a Solution

Apparently the Q caused by the bat is equal to the Q lost by the room, I'm just not sure how to calculate Qb and Qr (Qb being the Heat of the Bat, and Qr being the heat of the room), given that I don't have a final temperature.

I know it's super simple, but I'd love some clarity on the situation. Thanks!

 

[Andrew Mason]

Apparently the Q caused by the bat is equal to the Q lost by the room, I'm just not sure how to calculate Qb and Qr (Qb being the Heat of the Bat, and Qr being the heat of the room), given that I don't have a final temperature.

You have to determine Tf. You have all the information to do this.

Write out the equation for the heat flow into the bat (using the form of equation you have stated). That is your first equation. The unknown on the left side is Qb and on the right side the unknown is Tf.

Write out the equation for the heat flow out of the room (again using the same form of equation). That is your second equation. The unknowns are Qr and Tf.

Since, as you have said, the magnitudes of Qb and Qr are equal, you can reduce this to one equation with one unknown, Tf. Solve for Tf.

AM

 

[p1mpz0r]

Thank you thank you thank you :]

Turns out to be ~ 23.51 Celsius